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The Nursing Workforce - 2010

Appendix 2. Specification of the dynamic model

Registered nurses

We adopt index t to denote year, and k to denote k th age group of nurses. The variables are defined as following:

Formula : The number of nurses in the workforce in year t and age group k
Formula : The new nurse graduates – the number of new nurse graduates in year t and age group k,
Formula : The nurse exits – the number of nurses who leave the nurse workforce in year t and age group k ,
Formula : The nurse intake – the number of new nurses at work in year t and age group k .
Formula : The nurse intake due to immigration– the number of new overseas nurses at work in year t and age group k .
Formula : The nurse exit rate defined by Formula - the net proportion of nurses who leave from the nursing workforce in age group k and year t

The aggregate number of nurses, new nurse graduates, net exit, nurse intake and migrant nurses are:

The model is simply based on an identity: the annual increase of the number of nurses in the workforce (in year t and age group k ) must be equal to the net inflow of nurses (intake minus exit) into the workforce in the same year and the same age group10:

The first term on the right hand side of (A2.2) is due to ageing: the nurses of the previous year (t-1) in the younger age group (k-1) move to the age group k this year (t). The second term of (A2.2) in the bracket is the net influx of nurses in year t and age group k.

New nurses supplies can be expressed by

The value of each can be determined by fitting the historical data (see appendix 3) and each its value represents the corresponding proportion of the new graduates in previous years in entering into the nursing workforce at year t .

Our dynamic nurse model can first be used to obtain the historical net nurse exit rates. Using (A2.3) and rewriting (A2.2), we arrive at the nurse net exits:

The net nurse exit rates are then11

A proper modelling of (A2.5) requires Formula and G having the same age and year coverage. While the available data cover an entire age spectrum, we have only a limited number of years in overlap. Applicable data for new nurse graduates (G) starts only in 1995, so a reliable estimate of the exit rate only begins in 199512. Because of the absence of data O in 1998, a reliable x has to terminate in 1996.

Once the net exit rate is determined, we can substitute it in (A2.4) and obtain a formula for projection :

The aggregate exit rates, derived from (A2.4) and (A2.5a), are

Enrolled nurses

The limitation of the enrolled nurse graduate data prohibits us from adopting an identical approach as used previously for enrolled nurses. However, we can apply the same method at the aggregate level. The (net) aggregated exit rates each year can be obtained from (A2.4):

In (A2.7), we have assumed that there is no delay between course completion and being a nurse. This treatment makes the calculation easier. As we shall see in the appendix 3 that a mean exit rate over six years is adopted, this assumption does not affect much the projection for the enrolled nurses. Having obtained the exit rate (which is practically an average over a few years as can be seen in the Appendix 3), we can project enrolled nurses by

This is a linear projection given a constant aggregate exit rate, new graduate and migrant nurses. However, it can be argued that the workforce of enrolled nurses will age in a similar way to the workforce of registered nurses because of the resemblance of their initial age distributions. We can add the percentage point change of the aggregate exit rate derived from the registered nurse on to that of the enrolled nurses. Figure A2.1 projected aggregate exit rates for registered and enrolled nurses (2000-2020). This method is used in Table 4.3 to derive future aggregate exit rates for the enrolled nurses.

Figure A2.1 Projected aggregate exit rates for registered and enrolled nurses, 2000-2020

Figure A2.1 Projected aggregate exit rates for registered and enrolled nurses, 2000-2020

 


Foot Notes:

10.The continuous form of this difference equation is , with k here as a continuous variable to describe the date of birth. In discretising this equation with a time unit one year, O needs to be the final count of the number of nurses at the end of the year.

11.Note that we define the exit rate with lag in time and age group but this definition may be arbitrary.

12.In this case, an extrapolation of G before 1995 is still necessary, though this approximation is not crucial.

 

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